What is the true slope of a pavement if the longitudinal slope is 4% and the cross slope is 3%?

What is the true slope of a pavement if the longitudinal slope is 4% and the cross slope is 3%?

• A. 3%
• B. 4%
• C. 5%
• D. 7%

Answer: (C)

To determine the true slope of a pavement with both a longitudinal slope of 4% and a cross slope of 3%, you can visualize these slopes as components of a right triangle. The longitudinal slope represents one leg of the triangle, while the cross slope represents the other leg. To find the true slope, you need to calculate the hypotenuse, which can be done using the Pythagorean theorem. In this case, the longitudinal slope (4%) and the cross slope (3%) can be converted to decimal form (0.04 and 0.03, respectively). To find the true slope, you calculate the square root of the sum of the squares of these two slopes: True slope = √((0.04)² + (0.03)²) True slope = √(0.0016 + 0.0009) True slope = √(0.0025) True slope = 0.05 or 5%. Thus, the true slope of the pavement is 5%. This approach of using the Pythagorean theorem is essential when dealing with slopes because it accurately accounts for both dimensions of slope on a surface, providing a clearer understanding of the overall gradient.

To determine the true slope of a pavement with both a longitudinal slope of 4% and a cross slope of 3%, you can visualize these slopes as components of a right triangle. The longitudinal slope represents one leg of the triangle, while the cross slope represents the other leg. To find the true slope, you need to calculate the hypotenuse, which can be done using the Pythagorean theorem.

In this case, the longitudinal slope (4%) and the cross slope (3%) can be converted to decimal form (0.04 and 0.03, respectively). To find the true slope, you calculate the square root of the sum of the squares of these two slopes:

True slope = √((0.04)² + (0.03)²)

True slope = √(0.0016 + 0.0009)

True slope = √(0.0025)

True slope = 0.05 or 5%.

Thus, the true slope of the pavement is 5%. This approach of using the Pythagorean theorem is essential when dealing with slopes because it accurately accounts for both dimensions of slope on a surface, providing a clearer understanding of the overall gradient.